Cristiano Ronaldo is mobbed by team-mates after scoring the second of his two goals for Portugal against Holland. Photograph: Carl Recine/Action Images

Cristiano Ronaldo had waited more than a week to make his mark on the finals of Euro 2012. He had loitered ineffectively as Portugal fell to an opening defeat at the hands of Germany and he had missed two sitters as other men secured the victory over Denmark. On Sunday night, however, he came to the party.

He would like this to be his tournament, the one to consecrate his place among the immortals. The two goals that extinguished Holland's hopes were simply the statistical evidence of his influence on a match that finished 2-1. He also hit the post twice and manufactured chances that his team-mates should have put away with ease. He simply got down to the business of winning a match, minus the pouting and the shrugging and the melodramatic recriminations. He was every bit as good as he thinks he is.

This is certainly no tournament for faint hearts. While Germany went about the business of securing their passage to the quarter-finals against Denmark, also winning 2-1, Portugal and Holland battled for Group B's other slot in a contest entirely consistent with the thrills and spills that began in Warsaw on 8 June and show no sign of abating. Portugal will now play the Czech Republic in Warsaw on Thursday, while Germany play Greece in Gdansk the following day, in a match with a riveting human subtext.

If there is a lesson from the first 10 days of the competition, it is that fortune favours those willing to make the most of what they've got. In other words, just being Ronaldo or Robin van Persie is not enough. You have to turn up and impose yourself, as Portugal's captain finally did and Arsenal's, in the jersey of Holland, did not.

Sadly, and wholly unnecessarily, this is the last of Uefa's 16-team finals, a format sacrificed in order to placate nations wanting to improve their chance of a place at the feast. After the first two rounds of matches, only two teams – Sweden and the Republic of Ireland – had been given their tickets home. Everything else was still in play and on Saturday night, in the first set of final group matches, the sudden elimination of Russia and Poland, who had been widely expected to go through, again displayed the volatility and unpredictability of this tournament.

The tone had been set in the opening match when Poland took the lead against Greece in front of an expectant crowd in Warsaw but were dumbfounded by opponents who, reduced to 10 men for half the match, came back to seize what turned out to be a vital point. Since then there has barely been time to draw breath.

Ronaldo was seemingly determined to make up for his anonymous performance in Portugal's opening 1-0 defeat against Germany and for his profligacy in the 3-2 victory over Denmark. But it was not until Holland had taken the lead through a sumptuous strike from Rafael van der Vaart that he began to stir, hitting the base of a post from 20 yards before waiting as João Pereira drifted in from the right, sprinting to meet the perfect straight pass and clipping it past Maarten Stekelenburg from close range. Finally he had scored in these finals, a goal to add to his 60 for Real Madrid last season. And there would be more.

The Portuguese fans, even more heavily outnumbered by the Dutch than England's were by those of Sweden in Kiev last week, swooned in ecstasy. The orange hordes fell silent, knowing that Denmark, over in Lviv, were a long way from the victory that would have opened the way for Holland to join them in the knockout round.

In keeping with the tournament's spirit of adventure, Bert van Marwijk's way of celebrating Father's Day was to drop his son-in-law, Mark van Bommel, to the Dutch bench and to transfer the captaincy to Van der Vaart. The switch had been tried as a half-time substitution during the previous game, against Germany, and Holland had appeared to benefit from it, as they had from the arrival of Klaas Jan Huntelaar in place of Ibrahim Afellay, a change also repeated in Sunday's starting lineup.

It was a bold gesture and it paid off when Van der Vaart curled a fine shot around Rui Patrício in the 11th minute. The cost, however, became apparent in the minutes that followed when Portugal took advantage of Van Bommel's absence to tear into the unprotected Dutch defence. Ronaldo's first goal was the product of that sustained assault and there might have been others before half-time. He struck again with a quarter of an hour left, deftly controlling Nani's fine pass from the right before shifting his balance and guiding a right-footed shot inside the near post.

Van der Vaart struck a curler against the woodwork but by then Germany had scored a second goal against the Danes. Ronaldo had time to hit the post again, too, as Holland went out, the World Cup finalists of two years ago defeated in all three of their group matches. And you would not bet against there being more of this sort of thing to come before we are all very much older. And more, too, from a man who probably believes the tournament is now at his mercy.